Use the following sets to complete the givien statements in as many ways as possible.
a= a,b,c,d
b= e,f
c=b,a,c,d
d= 1,2,3,4
A. Sets _ and _ are not equivalent and not equal
B. Sets _ and _ are not equivalent but are equal.
C. Sets _and _ are equivalent but not equal
D. Sets _ and _ are equivalent and equal.
I just need you to check my answers.
A. A,b
B. impossible because all equal sets are equivalent
C. C,D
D. A,C
Do I have these right thanks
D is right, equivalent and equal
C is right, equivalent, but not equal
B correct. Has to be equivalent before it can be equal
A correct, but other answers are b,c or b,d
Thanks I was hopeing I understood this right thanks again
Let's go through each statement and check your answers:
A. Sets A and B are not equivalent and not equal.
Your answer: A, b
Explanation: To check if two sets are equivalent, we need to compare the elements in each set. In this case, set A contains a, b, c, and d, while set B contains e and f. Since these sets have different elements, they are not equivalent. Additionally, since they have different elements, they are also not equal. So your answer A, b is correct.
B. Sets C and D are not equivalent but are equal.
Your answer: impossible because all equal sets are equivalent
Explanation: This answer is incorrect. While it is true that all equal sets are also equivalent, there can still be sets that are equal but not equivalent if they have different elements. Let's compare sets C and D: Set C contains b, a, c, and d, while set D contains 1, 2, 3, and 4. These sets have different elements, but they have the same number of elements, so they are equal. Hence, the correct answer is C and D.
C. Sets A and C are equivalent but not equal.
Your answer: C, D
Explanation: To check if two sets are equivalent, we need to compare the elements in each set. Set A contains a, b, c, and d, while set C contains b, a, c, and d. Although the order of elements is different, these two sets have the same elements. Therefore, they are equivalent. However, since they have different orderings, they are not equal. So your answer C, D is correct.
D. Sets A and C are equivalent and equal.
Your answer: A, C
Explanation: This answer is incorrect. While sets A and C are indeed equivalent, they are not equal because they have a different ordering of elements. Set A contains a, b, c, and d, while set C contains b, a, c, and d. Since the ordering is different, they are not equal.
So, overall, you have the following answers correct:
A. A,b
C. C,D
Please double-check your statement B, as it can be true based on the given sets.